Connection.

[The Squatter of Amon Rûdh]

There's clearly a connection here, in that the Ring abandons and betrays both Gollum and Isildur; but the in the former case the abandonment and the betrayal to death are separated by a matter of decades. Gollum's death is more a fulfillment of the prophecy at RotK p.922 (HarperCollins single-volume edition): "If you touch me ever again, you shall be cast yourself into the Fire of Doom."

I think the real connection here is between Sauron and Frodo: the Ring's maker and its would-be destroyer. Sauron creates the Ring to enslave the world, which provokes the War of the Last Alliance and his eventual downfall. The Ring is forcibly taken from him. Frodo, although he begins with the intention of destroying the Ring, eventually claims it. In fact, his final attempt to claim the Ring seems intended to echo Many Meetings, where the following exchange takes place:

LR Book II ch. 1

'Hurray!' cried Pippin, springing up. 'Here is our noble cousin! Make way for Frodo, Lord of the Ring!'

'Hush!' said Gandalf from the shadows at the back of the porch. 'Evil things do not come into this valley; but all the same we should not name them. The Lord of the Ring is not Frodo, but the master of the Dark Tower of Mordor, whose power is again stretching out over the world!

Therefore when Frodo claims the Ring at the Sammath Naur, he assumes an ownership and title that is not his. In effect he tries to become a petty Sauron himself:

'But I do not choose now to do what I came to do. I will not do this deed. The Ring is mine!'

Therefore we can see the cutting of Frodo's finger as a deliberate parallel of Sauron's own injury. In effect Gollum's assault and the loss of Frodo's finger are a deliverance, but their nature reminds us that Frodo has, however briefly, desired to become as Sauron. In a small way his attempt has succeeded: like Sauron, he has lost a finger.

Then again, the parallel may be much simpler: the easiest way to remove a ring from a finger it is disinclined to leave is to cut off the finger. In the cases of both Isildur in the Last Alliance and Gollum at the Sammath Naur, the Ring had good reason to wish to stay on its current bearer's hand, so perhaps the only way to remove it was physically to remove the member on which it was worn. An interesting parallel is that the cases of Isildur and Gollum are alike and yet opposed: both revolve around possession of the Ring, but Isildur dies in losing it, Gollum in reclaiming it. It seems that the scene at the Sammath Naur is the closing of a circle: what began with the making of the Ring ends where that was achieved; what began when Isildur cut the Ring from Sauron's hand ends with Gollum biting it from Frodo's. This structure seems too premeditated to be simply coincidence, so I see it as an example of Tolkien's use of symmetry and dramatic opposition in The Lord of the Rings.

p.s. *bump*